SICP問題2.86
複素数で実部、虚部、絶対値および偏角が通常の数、有理数またはシステムに追加しようと思うかも知れぬ他の数であるものを扱うための変更。
複素数パッケージでschemeのプリミティブな関数を使わずに、定義したtag付の演算を使えばOKなはず。
有理数から実数への変換は手でやってたんですが、 truncateとかinexact->exactとかを使うみたいですね。
ということでその辺りも修正。
汎用手続きの追加。
(define (gene-square x) (apply-generic 'gene-square x)) (define (gene-sqrt x) (apply-generic 'gene-sqrt x)) (define (gene-atan x) (apply-generic 'gene-atan x)) (define (gene-sine x) (apply-generic 'gene-sine x)) (define (gene-cosine x) (apply-generic 'gene-cosine x)) (define (gene-sine x) (apply-generic 'gene-sine x))
それぞれの手続き
(define (install-integer-package) (define (tag x) (attach-tag 'integer x)) (define (integer->rational n) (make-rational n 1)) (put 'add '(integer integer) (lambda (x y) (tag (+ x y)))) (put 'sub '(integer integer) (lambda (x y) (tag (- x y)))) (put 'mul '(integer integer) (lambda (x y) (tag (* x y)))) (put 'div '(integer integer) (lambda (x y) (tag (/ x y)))) (put 'equ? '(integer integer) (lambda (x y) (= x y))) (put '=zero? '(integer) (lambda (x) (= x 0))) (put 'make 'integer (lambda (x) (tag x))) (put 'exp '(integer integer) (lambda (x y) (tag (expt x y)))) (put 'raise 'integer (lambda (x) (integer->rational x))) ;; 追加 (put 'gene-square '(integer) (lambda (x) (tag (* x x)))) (put 'gene-sqrt '(integer) (lambda (x) (tag (sqrt x)))) (put 'gene-atan '(integer) (lambda (x) (tag (atan x)))) (put 'gene-cosine '(integer) (lambda (x) (tag (cos x)))) (put 'gene-sine '(integer) (lambda (x) (tag (sin x)))) 'done) (install-integer-package) (define (make-integer n) ((get 'make 'integer) n)) ; 有理数算術演算 (define (install-rational-package) (define (numer x) (car x)) (define (denom x) (cdr x)) (define (make-rat n d) (let ((g (gcd n d))) (cons (/ n g) (/ d g)))) (define (add-rat x y) (make-rat (+ (* (numer x) (denom y)) (* (numer y) (denom x))) (* (denom x) (denom y)))) (define (sub-rat x y) (make-rat (- (* (numer x) (denom y)) (* (numer y) (denom x))) (* (denom x) (denom y)))) (define (mul-rat x y) (make-rat (* (numer x) (numer y)) (* (denom x) (denom y)))) (define (div-rat x y) (make-rat (* (numer x) (denom y)) (* (denom x) (numer y)))) (define (equ-rat x y) (= (* (numer x) (denom y)) (* (numer y) (denom x)))) (define (=zero-rat x) (and (= (numer x) 0) (not (= (denom x) 0)))) ;; 追加 (define (gene-square-rat x) (make-rat (* (numer x) (numer x)) (* (denom x) (denom x)))) (define (gene-sqrt-rat x) ; inexact->exact方式(小数点以下 5桁位の精度で) (make-rat (inexact->exact (truncate (* 100000 (sqrt (/ (numer x) (denom x)))))) 100000)) (define (gene-atan-rat x) ; inexact->exact方式(小数点以下 5桁位の精度で) (make-rat (inexact->exact (truncate (* 100000 (atan (/ (numer x) (denom x)))))) 100000)) (define (gene-cosine-rat x) ; inexact->exact方式(小数点以下 5桁位の精度で) (make-rat (inexact->exact (truncate (* 100000 (cos (/ (numer x) (denom x)))))) 100000)) (define (gene-sine-rat x) ; inexact->exact方式(小数点以下 5桁位の精度で) (make-rat (inexact->exact (truncate (* 100000 (sin (/ (numer x) (denom x)))))) 100000)) ;; システムの他の部分へのインタフェース (define (tag x) (attach-tag 'rational x)) (define (rational->real x) (make-real (/ (numer x) (denom x)))) (define (rational->integer x) (make-integer (round (/ (numer x) (denom x))))) (put 'add '(rational rational) (lambda (x y) (tag (add-rat x y)))) (put 'sub '(rational rational) (lambda (x y) (tag (sub-rat x y)))) (put 'mul '(rational rational) (lambda (x y) (tag (mul-rat x y)))) (put 'div '(rational rational) (lambda (x y) (tag (div-rat x y)))) (put 'equ? '(rational rational) (lambda (x y) (equ-rat x y))) (put '=zero? '(rational) (lambda (x) (=zero-rat x))) (put 'make 'rational (lambda (n d) (tag (make-rat n d)))) (put 'raise 'rational (lambda (x) (rational->real x))) (put 'project 'rational (lambda (x) (rational->integer x))) ;; 追加 (put 'gene-square '(rational) (lambda (x) (tag (gene-square-rat x)))) (put 'gene-sqrt '(rational) (lambda (x) (tag (gene-sqrt-rat x)))) (put 'gene-atan '(rational) (lambda (x) (tag (gene-atan-rat x)))) (put 'gene-cosine '(rational) (lambda (x) (tag (gene-cosine-rat x)))) (put 'gene-sine '(rational) (lambda (x) (tag (gene-sine-rat x)))) 'done) (define (make-rational n d) ((get 'make 'rational) n d)) ;; 実数パッケージ (define (install-real-package) (define (tag x) (attach-tag 'real x)) (define (real->complex x) (make-complex-from-real-imag x 0)) ; ; inexact->exact方式(小数点以下 5桁位の精度で) (define (real->rational x) (make-rational (inexact->exact (round (* x 100000))) 100000)) (put 'add '(real real) (lambda (x y) (tag (+ x y)))) (put 'sub '(real real) (lambda (x y) (tag (- x y)))) (put 'mul '(real real) (lambda (x y) (tag (* x y)))) (put 'div '(real real) (lambda (x y) (tag (/ x y)))) (put 'equ? '(real real) (lambda (x y) (= x y))) (put '=zero? '(real) (lambda (x) (= x 0))) ; exact->inexcat方式に変更 (put 'make 'real (lambda (x) (tag (exact->inexact x)))) (put 'exp '(real real) (lambda (x y) (tag (expt x y)))) (put 'raise 'real (lambda (x) (real->complex x))) (put 'project 'real (lambda (x) (real->rational x))) ;; 追加 (put 'gene-square '(real) (lambda (x) (tag (* x x)))) (put 'gene-sqrt '(real) (lambda (x) (tag (sqrt x)))) (put 'gene-atan '(real) (lambda (x) (tag (atan x)))) (put 'gene-cosine '(real) (lambda (x) (tag (cos x)))) (put 'gene-sine '(real) (lambda (x) (tag (sin x)))) 'done) (install-real-package) (define (make-real x) ((get 'make 'real) x)) ; 複素数の直交座標パッケージと極座標パッケージ ; 直行座標 (define (install-rectangular-package) ;;内部手続き (define (real-part z) (car z)) (define (imag-part z) (cdr z)) (define (make-from-real-imag x y) (cons x y)) (define (magnitude z) (gene-sqrt (add (gene-square (real-part z)) ;; 変更 (gene-square (imag-part z))))) ;; 変更 (define (angle z) (gene-atan (mul (imag-part z) (real-part z)))) ;; 変更。いまいちatanの使い方分かってないけど (define (make-from-mag-ang r a) (cons (* r (gene-cosine a)) (* r (gene-sine a)))) ;; システムの他の部分とのインタフェース (define (tag x) (attach-tag 'rectangular x)) (put 'real-part '(rectangular) real-part) (put 'imag-part '(rectangular) imag-part) (put 'magnitude '(rectangular) magnitude) (put 'angle '(rectangular) angle) (put 'make-from-real-imag 'rectangular (lambda (x y) (tag (make-from-real-imag x y)))) (put 'make-from-mag-ang 'rectangular (lambda (r a) (tag (make-from-mag-ang r a)))) 'done) ; 極座標の場合 (define (install-polar-package) ;;内部手続き (define (magnitude z) (car z)) (define (angle z) (cdr z)) (define (make-from-mag-ang r a) (cons r a)) (define (real-part z) (mul (magnitude z) (gene-cosine (angle z)))) ;;変更 (define (imag-part z) (mul (magnitude z) (gene-sine (angle z)))) ;;変更 (define (make-from-real-imag x y) (cons (gene-sqrt (+ (gene-square x) (gene-square y))) (gene-atan y x))) ;; システムの他の部分とのインタフェース (define (tag x) (attach-tag 'polar x)) (put 'real-part '(polar) real-part) (put 'imag-part '(polar) imag-part) (put 'magnitude '(polar) magnitude) (put 'angle '(polar) angle) (put 'make-from-real-imag 'polar (lambda (x y) (tag (make-from-real-imag x y)))) (put 'make-from-mag-ang 'polar (lambda (r a) (tag (make-from-mag-ang r a)))) 'done) ; apply-generic を使った汎用選択子の定義 (define (real-part z) (apply-generic 'real-part z)) (define (imag-part z) (apply-generic 'imag-part z)) (define (magnitude z) (apply-generic 'magnitude z)) (define (angle z) (apply-generic 'angle z)) ; パッケージの外部のプログラムから、それぞれの構成子を使用する (define (make-from-real-imag x y) ((get 'make-from-real-imag 'rectangular) x y)) (define (make-from-mag-ang r a) ((get 'make-from-mag-ang 'polar) r a)) ; 複素数 (define (install-complex-package) ;; 直交座標と極座標パッケージから取り入れた手続き (define (make-from-real-imag x y) ((get 'make-from-real-imag 'rectangular) x y)) (define (make-from-mag-ang r a) ((get 'make-from-mag-ang 'polar) r a)) ;; 内部手続き この辺りを変更 (define (add-complex z1 z2) (make-from-real-imag (add (real-part z1) (real-part z2)) (add (imag-part z1) (imag-part z2)))) (define (sub-complex z1 z2) (make-from-real-imag (sub (real-part z1) (real-part z2)) (sub (imag-part z1) (imag-part z2)))) (define (mul-complex z1 z2) (make-from-real-imag (mul (magnitude z1) (magnitude z2)) (mul (angle z1) (angle z2)))) (define (div-complex z1 z2) (make-from-real-imag (div (magnitude z1) (magnitude z2)) (sub (angle z1) (angle z2)))) (define (equ-complex z1 z2) (and (equ? (real-part z1) (real-part z2)) (equ? (imag-part z1) (imag-part z2)))) (define (=zero-complex z) (and (equ? (real-part z) 0) (equ? (imag-part z) 0))) (define (complex->real z) (make-real (real-part z))) ;; システムの他の部分へのインタフェース (define (tag z) (attach-tag 'complex z)) (put 'add '(complex complex) (lambda (z1 z2) (tag (add-complex z1 z2)))) (put 'sub '(complex complex) (lambda (z1 z2) (tag (sub-complex z1 z2)))) (put 'mul '(complex complex) (lambda (z1 z2) (tag (mul-complex z1 z2)))) (put 'div '(complex complex) (lambda (z1 z2) (tag (div-complex z1 z2)))) (put 'make-from-real-imag 'complex (lambda (x y) (tag (make-from-real-imag x y)))) (put 'make-from-mag-ang 'complex (lambda (r a) (tag (make-from-mag-ang r a)))) (put 'equ? '(complex complex) (lambda (z1 z2) (equ-complex z1 z2))) (put '=zero? '(complex) (lambda (x) (=zero-complex x))) (put 'real-part '(complex) real-part) (put 'imag-part '(complex) imag-part) (put 'magnitude '(complex) magnitude) (put 'ange '(complex) angle) (put 'project 'complex (lambda (x) (complex->real x))) 'done) (define (make-complex-from-real-imag x y) ((get 'make-from-real-imag 'complex) x y)) (define (make-complex-from-mag-ang r a) ((get 'make-from-mag-ang 'complex) r a)) (install-integer-package) (install-rational-package) (install-real-package) (install-rectangular-package) (install-polar-package) (install-complex-package)
軽くテスト
(add (make-complex-from-real-imag (make-real 3.5) (make-real 4.5)) (make-complex-from-real-imag (make-real 4.2) (make-real 4.1))) ; (complex rectangular (real . 7.7) real . 8.6) (mul (make-complex-from-real-imag (make-real 3.5) (make-real 4.5)) (make-complex-from-real-imag (make-real 4.2) (make-real 4.1))) ; (complex rectangular (real . 33.46079795820778) real . 2.2803627668061783) (add (make-complex-from-real-imag (make-rational 3 6) (make-real 4.5)) (make-complex-from-real-imag (make-real 4.2) (make-real 4.1))) ; (complex rectangular (rational 47 . 10) real . 8.6) (mul (make-complex-from-mag-ang (make-real 3.5) (make-real 4.0)) (make-complex-from-mag-ang (make-real 3.5) (make-real 4.0))) ; (complex rectangular (real . 12.25) real . 16.0) (add (make-complex-from-mag-ang (make-rational 3 5) (make-rational 4 3)) (make-complex-from-mag-ang (make-rational 3 4) (make-rational 5 4))) ; (complex rectangular (rational 94407 . 250000) rational 1294893 . 1000000)
いまいちうまく行ってない感じもしますが、とりあえずOKということで。